{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Updating with Conjugate Priors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the data consists of binary Bernoulli random variables with a certain success probability for a positive outcome, the number of successes in repeated trials follows a Binomial distribution. The conjugate prior is the Beta distribution with support over the interval [0, 1] and two shape parameters to model arbitrary prior distributions over the success probability. Hence, the posterior distribution is also a Beta distribution that we can derive by directly updating the parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T20:25:06.885204Z",
     "start_time": "2018-12-27T20:25:06.872783Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "import scipy.stats as stats\n",
    "from matplotlib.ticker import FuncFormatter\n",
    "import warnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T20:25:06.896054Z",
     "start_time": "2018-12-27T20:25:06.888545Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "mpl.rcParams['text.usetex'] = True\n",
    "mpl.rcParams['text.latex.preamble'] = [r'\\usepackage{amsmath}']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T20:25:06.904258Z",
     "start_time": "2018-12-27T20:25:06.898183Z"
    }
   },
   "outputs": [],
   "source": [
    "warnings.filterwarnings('ignore')\n",
    "np.random.seed(42)\n",
    "sns.set_style('dark')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formatting Helper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T20:25:06.912946Z",
     "start_time": "2018-12-27T20:25:06.906098Z"
    }
   },
   "outputs": [],
   "source": [
    "def format_plot(axes, i, p, y, trials, success, true_p, tmle, tmap=None):\n",
    "    fmt = FuncFormatter(lambda x, _: f'{x:.0%}')\n",
    "    if i >= 6:\n",
    "        axes[i].set_xlabel(\"$p$, Success Probability\")\n",
    "        axes[i].xaxis.set_major_formatter(fmt)\n",
    "    else:\n",
    "        axes[i].axes.get_xaxis().set_visible(False)\n",
    "    if i % 3 == 0:\n",
    "        axes[i].set_ylabel(\"Posterior Probability\")\n",
    "    axes[i].set_yticks([], [])\n",
    "\n",
    "    axes[i].plot(p, y, lw=1, c='k')\n",
    "    axes[i].fill_between(p, y, color='darkblue', alpha=0.4)\n",
    "    axes[i].vlines(true_p, 0, max(10, np.max(y)), color='k', linestyle='--', lw=1)\n",
    "    axes[i].set_title(f'Trials: {trials:,d} - Success: {success:,d}')\n",
    "    if i > 0:\n",
    "        smle = r\"$\\theta_{{\\mathrm{{MLE}}}}$ = {:.2%}\".format(tmle)\n",
    "        axes[i].text(x=.02, y=.85, s=smle, transform=axes[i].transAxes)\n",
    "        smap = r\"$\\theta_{{\\mathrm{{MAP}}}}$ = {:.2%}\".format(tmap)\n",
    "        axes[i].text(x=.02, y=.75, s=smap, transform=axes[i].transAxes)    \n",
    "    return axes[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate Coin Tosses & Updates of Posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T20:25:08.679250Z",
     "start_time": "2018-12-27T20:25:06.913980Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x504 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_trials = [0, 1, 3, 5, 10, 25, 50, 100, 500]\n",
    "outcomes = stats.bernoulli.rvs(p=0.5, size=n_trials[-1])\n",
    "p = np.linspace(0, 1, 100)\n",
    "# uniform (uninformative) prior\n",
    "a = b = 1\n",
    "\n",
    "fig, axes = plt.subplots(nrows=3, ncols=3, figsize=(14, 7), sharex=True)\n",
    "axes = axes.flatten()\n",
    "fmt = FuncFormatter(lambda x, _: f'{x:.0%}')\n",
    "for i, trials in enumerate(n_trials):\n",
    "    successes = outcomes[:trials]\n",
    "    theta_mle = np.mean(successes)\n",
    "    heads = sum(successes)\n",
    "    tails = trials - heads\n",
    "    update = stats.beta.pdf(p, a + heads , b + tails)\n",
    "    theta_map = pd.Series(update, index=p).idxmax()\n",
    "    axes[i] = format_plot(axes, i, p, update, trials=trials, success=heads, \n",
    "                          true_p=.5, tmle=theta_mle, tmap=theta_map)\n",
    "\n",
    "title = 'Bayesian Probabilities: Updating the Posterior'\n",
    "fig.suptitle(title,  y=1.02, fontsize=14)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stock Price Moves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will collect samples of different sizes of binarized daily S&P 500 returns where the positive outcome is a price increase. Starting from an uninformative prior that allocates equal probability to each possible success probability in the interval [0, 1], we compute the posterior for different evidence samples. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T20:25:08.774355Z",
     "start_time": "2018-12-27T20:25:08.680972Z"
    }
   },
   "outputs": [],
   "source": [
    "sp500_returns = pd.read_hdf('../data/assets.h5', key='sp500/prices').loc['2010':, 'close']\n",
    "sp500_binary = (sp500_returns.pct_change().dropna() > 0).astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code sample shows that the update consists in simply adding the observed numbers of success and failure to the parameters of the prior distribution to obtain the posterior.\n",
    "\n",
    "The resulting posterior distributions are plotted below. They illustrate the evolution from a  uniform prior that views all success probabilities as equally likely to an increasingly peaked distribution.\n",
    "After 500 samples, the probability is concentrated near the actual probability of a positive move at 54.7% from 2010 to 2017. It also shows the small differences between MLE and MAP estimates, where the latter tends to be pulled slightly towards the expected value of the uniform prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T20:25:22.630925Z",
     "start_time": "2018-12-27T20:25:21.953368Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_days = [0, 1, 3, 5, 10, 25, 50, 100, 500]\n",
    "# random sample of trading days\n",
    "# outcomes = sp500_binary.sample(n_days[-1])\n",
    "\n",
    "# initial 500 trading days\n",
    "outcomes = sp500_binary.iloc[:n_days[-1]]\n",
    "p = np.linspace(0, 1, 100)\n",
    "\n",
    "# uniform (uninformative) prior\n",
    "a = b = 1\n",
    "\n",
    "fig, axes = plt.subplots(nrows=3, ncols=3, figsize=(14, 7), sharex=True)\n",
    "axes = axes.flatten()\n",
    "for i, days in enumerate(n_days):\n",
    "    successes = outcomes.iloc[:days]\n",
    "    theta_mle = successes.mean()\n",
    "    up = successes.sum()\n",
    "    down = days - up\n",
    "    update = stats.beta.pdf(p, a + up , b + down)\n",
    "    theta_map = pd.Series(update, index=p).idxmax()\n",
    "    axes[i] = format_plot(axes, i, p, update, trials=days, success=up, \n",
    "                          true_p=sp500_binary.mean(), tmle=theta_mle, tmap=theta_map)\n",
    "\n",
    "title = 'Bayesian Probabilities: Updating the Posterior'\n",
    "fig.suptitle(title,  y=1.02, fontsize=14)\n",
    "fig.tight_layout()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
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  "toc": {
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   "number_sections": true,
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   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
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  }
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